The present invention relates to a new and distinct primocane bearing (fall bearing) red raspberry variety designated as ‘Crimson Giant.’ The variety is botanically known as Rubus idaeus L. The new and distinct variety of red raspberry originated from a hand-pollinated cross of the patented variety ‘Titan’ (patented as N.Y. 883, U.S. Plant Pat. No. 5,404) and Cornell selection NY950 (unpatented), which cross was made and the resulting seedling grown in Geneva, N.Y. The seedling, NY99-45, was selected from a controlled breeding plot in 1999. The new variety has been asexually propagated by dormant canes since 2000 and was established in tissue culture for propagation of plants for trials in 2006. This propagation has demonstrated that the combination of traits that characterize this variety are fixed and remain true to type through successive generations of asexual propagation. NY99-45 is being named and released as ‘Crimson Giant’ and is the subject of this invention.